Stale 'running task' indicator after response completes

Description

The task indicator shows \"1 running task\" even after a response has fully completed and no background tasks were spawned.

Steps to reproduce

1. Send a message that results in a normal (non-background) response
2. Observe the task indicator showing \"1 running task\" after the response is done
3. No background agents or tasks were started in the session

Expected behavior

The indicator clears when the response is complete and there are no active background tasks.

Actual behavior

\"1 running task\" remains visible indefinitely after the response, giving the impression something is still running when it is not.

Environment

• Claude Code desktop app (Mac)
• Session had no spawned background agents